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The Hypster Hyperchaos generator with VC
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Author The Hypster Hyperchaos generator with VC
frijitz
Hello --

Here is a writeup on my latest chaos generator circuit. It's fourth-order hyperchaotic, with voltage control of the main parameters, including exponential control of the cycle rate.

Ian

Edit: 16 Jan 2018
wackelpeter
Marvellous!

This really looks fantastic as all your other designs, great benefit for the DIY community as always. Thanks for all your efforts, they're pretty much appreciated.

Docs saved and hopefully within the next weeks i'm back at my soldering station and give it a try.

Cheers
Bastian
frijitz
wackelpeter wrote:
Marvellous!

This really looks fantastic as all your other designs, great benefit for the DIY community as always. Thanks for all your efforts, they're pretty much appreciated.

Docs saved and hopefully within the next weeks i'm back at my soldering station and give it a try.

Cheers
Bastian

Thanks! I'm really looking forward to having someone try it out. Please keep us posted. I worked pretty hard to make sure the schematics are correct, but with such a large unit there is always the possibility something got written down wrong. So please don't hesitate to ask if you have questions.

Ian
wackelpeter
Had spotted one minor error, you wrote LM1370 forgetting an 0.

One question i have, do i get it correct that the U' Output from A3 goes to ZD3 and X' to R1? Or when i'm using one of the shapers then this X' Output instead of the "normal" X' Output to R1 (82K)?
Btw. with an further Switch it should also be possible to choose between both X' outs correct?


For the schematics i'm sure there are others here more qualified than myself. The most (if not all) errors i had so far, were due to my own failures.

Don't know yet, if i can fit it all into one bigger stripboard or use a "double decker".

Well again, thanks for taking so much effort and enthusiasm into your work.

Cheers
Bastian

Edit: Ok i see at the block Diagramm both X' Outputs would be connected to R1 when i use the optional shaper, if i'm not totally wrong.
frijitz
wackelpeter wrote:
Had spotted one minor error, you wrote LM1370 forgetting an 0.

Arrgh! Thanks!
Quote:

One question i have, do i get it correct that the U' Output from A3 goes to ZD3 and X' to R1? Or when i'm using one of the shapers then this X' Output instead of the "normal" X' Output to R1 (82K)?
Btw. with an further Switch it should also be possible to choose between both X' outs correct?

The points with the little circles are connected together internally, per their labels. So yes, U' goes to ZD3, and -X' goes to R1 and (R97 or R98) depending on which shape option, etc. The double arrow points are panel I/O. Sure, if you want to build both shape options, then a switch between -X' of A16 out and either of the shapers R97/R98 would be appropriate.

Ian
slow_riot
Thanks for sharing your work, Ian. I studied it all. I did not like the lack of edges to chaos theory, and got more interested in turbulence, which are a more tuned sort of expression with parallel feedback paths within multiple equations. Look forward to investigating the material in this one too, of course.

I published the technique I used to stabilize complex analogue equations using high resolution RMS to DC conversion with variable time constant here:

It's only cost effective to use around 1 integrator, which does tend to upset the balance of how energy is shared in the system, but the overall stability is good.

https://aether-machine.com/rms-stabilization-of-oscillators/
emmaker
Ian, thanks for doing this. I've enjoyed and appreciate all the work that you've done in with chaos.

This is just a nit but for U1 and A11 the +/- inputs are different than the other op-amps and OTAs. For people paying attention that's fine but I tend to assume that the +/- inputs are drawn all the same. So if I wasn't paying attention I'd wire up things incorrectly. Maybe changing these or adding a note on that might help.

Lastly would circuit benefit from multi-turn pots for the damping and rate like the jerkster and double well chaos circuits?

Thank you.
Jay S.
notmiserlouagain
emmaker wrote:
Ian, thanks for doing this. I've enjoyed and appreciate all the work that you've done in with chaos.
Thank you.


+1 Mr. Fritz this is beautiful. And as you seem to be less interested in nice words than people building your circuits, I´ll start laying out a self etch pcb for this circuit this evening and will hopefully post it here (OK, only nice words again, let´s wait and see hihi ).

Cheers
trip
Wow, really inspiring work. Thank you for sharing.

Will give this a go as soon as some breadboards are freed up - looks like it will take a fair bit of space to build!
trip
The only thing I noticed in the schematic that might be a mistake is the orientation of A11, is that intentional? Still trying to figure out what's going on there.
notmiserlouagain
The lower section of the first schem is the CV-processing part, the upper part of the first and the second schem are basically four nonlinear sections, integrators and output inverters in a loop with a gain stage inbetween.
I don´t think A11 is wrong, just a different nonlinearity...
stringsthings
This circuit looks really cool. I'm hoping someone turns it into a PCB that I can purchase.
frijitz
slow_riot wrote:
Thanks for sharing your work, Ian. I studied it all. I did not like the lack of edges to chaos theory, and got more interested in turbulence, which are a more tuned sort of expression with parallel feedback paths within multiple equations. Look forward to investigating the material in this one too, of course.

I published the technique I used to stabilize complex analogue equations using high resolution RMS to DC conversion with variable time constant here:

It's only cost effective to use around 1 integrator, which does tend to upset the balance of how energy is shared in the system, but the overall stability is good.

https://aether-machine.com/rms-stabilization-of-oscillators/

Hi s_r --

Thanks for the interesting post! The THAT RMS chip looks very interesting. I remember seeing it, but I guess I missed the part about the current-controlled time constant. This could have a lot of interesting applications -- they've been running through my head all night.

As far as limiting excursions in chaos circuits -- well, this will take some more thought. The potential issue I see is that the excursions that saturate the system are often from the burstiness of the attractors. I'm not seeing how to catch those without really altering the attractor overall. I've seen attractors that chug along inside well-defined bounds for minutes before suddenly jumping into a bursty mode, then jumping back. If one of those sends the system to the rails, it's hard to manage. But it's an interesting idea, and I'll keep thinking about it.

The limiter in the present system works by preventing the system gain from getting too large relative to the damping. There is a bit of tradeoff vis a vis some of the more complex patterns, but there is still plenty of variety to be had. A couple of resistors and diodes seems a pretty cost-effective way to handle the problem, vs a solution using comparators.

I've been thinking about time-delay chaos lately. The texts I studied didn't really go into this, but a couple of literature papers I've run across look interesting. And member Tronketz has shown some interesting results in simulations using large phase delays in feedback configurations. Maybe a lagged RMS detector fed back to a control input could be fun.

As far as chaos not being all that edgy, I understand what you are saying -- all those integrators tend to round everything out. Since my main interest is in generating slow CV signals this doesn't bother me. At audio, bursty behavior sounds pretty edgy. And the audio can easily be processed with waveshapers or fast S/H's to get a wider range of harmonic content. Or try listening to Poincare sections! Is there a link for how you implemented turbulence? (Of course recognizing that turbulence is a kind of chaos.)

Ian
frijitz
emmaker wrote:
Ian, thanks for doing this. I've enjoyed and appreciate all the work that you've done in with chaos.

This is just a nit but for U1 and A11 the +/- inputs are different than the other op-amps and OTAs. For people paying attention that's fine but I tend to assume that the +/- inputs are drawn all the same. So if I wasn't paying attention I'd wire up things incorrectly. Maybe changing these or adding a note on that might help.

Lastly would circuit benefit from multi-turn pots for the damping and rate like the jerkster and double well chaos circuits?

Thank you.
Jay S.

Hi Jay --

Thanks for the careful look at the schematic! I drew the nonlinear sections with the nonlinear diodes going to the uppermost terminals. This was done for esthetic consistency and for consistency with how my spreadsheet equations were laid out. I didn't even realize that only the one amp was oriented with (+) on top! Could be confusing to some and might even look like an oopsie, but I've never seen a rule that says all amps have to be the same orientation. In fact, I just took a quick look at several textbooks, manufacturer data books and newsletters, and I don't see that convention followed anywhere.

The control I cleverly labeled Trim is a fine adjustment of Gain. It seems to serve well generally for tweaking the patterns, especially if you want to zero in on one that is stable only over a small range. Sure, put in Fine controls or 10-turns on both sections if you like. All those were left off the Euro Chaotica, and there haven't been any complaints. My impression is that most folks use the chaos modules in a fairly coarse manner, but myself, I like more subtle adjustments. There are more rapid changes in the patterns with the controls than in the lower-order systems, though, so I really suggest including at least the Trim adjustment as shown.

Ian
Dcramer
Gads woah must has finished module to complete my set w00t
frijitz
trip wrote:
Wow, really inspiring work. Thank you for sharing.

Will give this a go as soon as some breadboards are freed up - looks like it will take a fair bit of space to build!


trip --

Thanks! Yeah, it's pretty big. I ran out of room on my whiteboard, so I transfered it all to perfboard and finished up on the whiteboard. Then there wasn't enough room for everything on the perfboard, so I had to screw on an extension.

Ian
frijitz
Dcramer wrote:
Gads woah must has finished module to complete my set w00t

DC --
Yes, I agree, you must. thumbs up

As Rossler noted in his original hyperchaos research, it sounds different. His comment was it's more like rain falling on your car that the for the third order systems. Definitely can be very spitty and bursty at audio. For CV work like yours, it has, IMO, a much better variety of patterns, especially, as you can see, of the loopy, multiperiodic type.

I'm hoping for a partner to commercialize -- there was one guy interested, but he seems to have disappeared down a rabbit hole.

Ian
acgenerator
stringsthings wrote:
This circuit looks really cool. I'm hoping someone turns it into a PCB that I can purchase.


Would also be interested in a PCB + Panel set should a fabricator manifest themselves.
slow_riot
frijitz wrote:

Hi s_r --

Thanks for the interesting post! The THAT RMS chip looks very interesting. I remember seeing it, but I guess I missed the part about the current-controlled time constant. This could have a lot of interesting applications -- they've been running through my head all night.

As far as limiting excursions in chaos circuits -- well, this will take some more thought. The potential issue I see is that the excursions that saturate the system are often from the burstiness of the attractors. I'm not seeing how to catch those without really altering the attractor overall. I've seen attractors that chug along inside well-defined bounds for minutes before suddenly jumping into a bursty mode, then jumping back. If one of those sends the system to the rails, it's hard to manage. But it's an interesting idea, and I'll keep thinking about it.

The limiter in the present system works by preventing the system gain from getting too large relative to the damping. There is a bit of tradeoff vis a vis some of the more complex patterns, but there is still plenty of variety to be had. A couple of resistors and diodes seems a pretty cost-effective way to handle the problem, vs a solution using comparators.

I've been thinking about time-delay chaos lately. The texts I studied didn't really go into this, but a couple of literature papers I've run across look interesting. And member Tronketz has shown some interesting results in simulations using large phase delays in feedback configurations. Maybe a lagged RMS detector fed back to a control input could be fun.

As far as chaos not being all that edgy, I understand what you are saying -- all those integrators tend to round everything out. Since my main interest is in generating slow CV signals this doesn't bother me. At audio, bursty behavior sounds pretty edgy. And the audio can easily be processed with waveshapers or fast S/H's to get a wider range of harmonic content. Or try listening to Poincare sections! Is there a link for how you implemented turbulence? (Of course recognizing that turbulence is a kind of chaos.)

Ian


The variable time constant is a game changer for my use in stabilizing complex equations, especially at audio rates where classic limiting techniques impact the sound. I had not thought about more experimental usage of the technique and would be keen to see more. It has to be mentioned that for this computation there is a lot of processing power being done very efficiently, so it's nice to have a chance to give the digital world a run for it's money for once.

It may be more difficult to get it to work with chaos type circuits, although many differential equations do represent an equililbrium, no matter how unpredictable they may be.

Regarding turbulence, I have been looking into solving partial differential equations by analogue means and made good progress. I have working models for incompressible fluid flow, and oscillation of a circular membrane (wave equation). What unlocked the technique was getting around the need for generalized integration, where in any ODE the integration is done with respect to time, however in a PDE you also need to integrate with respect to different variables. These moments seem to happen frequently where you reach the edge of the theory where the industry abandoned their work to court digital techniques. Funnily enough, you can integrate with respect to a different variable than time by just assuming your non time variable can be represented by some relation to time, and an ordinary capacitance based integrator is just fine. In the audio field we don't need to accurately represent spatial or other variables so the substitution comes with no penalty (assuming the relationship between time and space is linear, of course).
glennfin
I'm not sure but..... The dark arrows (top of the pots) connect to +V?

.....also, U4, U5, U6 the dark arrow pointing to these op-amps, what pin? +v rail?..... and the "X Y Z" are the outputs? Are these quad opamps? singles? what type did you use? TL074"s?

I'm thinking about breadboarding this but want to make sure I understand the all the connections.

Thanks.
wackelpeter
glennfin wrote:
I'm not sure but..... The dark arrows (top of the pots) connect to +V?

.....also, U4, U5, U6 the dark arrow pointing to these op-amps, what pin? +v rail?..... and the "X Y Z" are the outputs? Are these quad opamps? singles? what type did you use? TL074"s?

I'm thinking about breadboarding this but want to make sure I understand the all the connections.

Thanks.



Yes the dark arrows at the pots are connected to Ub+ (V+).

U1-U6 are OTA (LM13700,13600 or CA3080) these are the bias Inputs (1 and 16 on 13600+13700 or pin 5 on LM or CA3080. Means you will Need either 6 CA3080 or 3 of the LM13x00 dual OTA.

The TL07x means you can take whatever TL07xx OpAmp you have at hand there... You can use a single, dual or quad opAmp, depends on your taste and those available.

Actually there are 8 Outputs U,X,Y,Z and their inverted function -U,-X and so on.


A quick question to Ian, the rate control of this circuit should be useful for the Jerkster too, correct? I'm asking because i'm having sometimes hard times to find a sweet spot at the rate Settings and it goes easily with just a slight turn very fast. Already have increased the resistors for the Bias Input but not a multi-turn pot until now. Would this improve things a bit or should i go for an multiturn pot instead? Or perhaps change both?

Cheers Bastian
glennfin
Thanks for the clarification Bastian. cool ... sorry I should have looked closer.. hmmm.....

wackelpeter wrote:
glennfin wrote:
I'm not sure but..... The dark arrows (top of the pots) connect to +V?

.....also, U4, U5, U6 the dark arrow pointing to these op-amps, what pin? +v rail?..... and the "X Y Z" are the outputs? Are these quad opamps? singles? what type did you use? TL074"s?

I'm thinking about breadboarding this but want to make sure I understand the all the connections.

Thanks.



Yes the dark arrows at the pots are connected to Ub+ (V+).

U1-U6 are OTA (LM13700,13600 or CA3080) these are the bias Inputs (1 and 16 on 13600+13700 or pin 5 on LM or CA3080. Means you will Need either 6 CA3080 or 3 of the LM13x00 dual OTA.

The TL07x means you can take whatever TL07xx OpAmp you have at hand there... You can use a single, dual or quad opAmp, depends on your taste and those available.

Actually there are 8 Outputs U,X,Y,Z and their inverted function -U,-X and so on.


A quick question to Ian, the rate control of this circuit should be useful for the Jerkster too, correct? I'm asking because i'm having sometimes hard times to find a sweet spot at the rate Settings and it goes easily with just a slight turn very fast. Already have increased the resistors for the Bias Input but not a multi-turn pot until now. Would this improve things a bit or should i go for an multiturn pot instead? Or perhaps change both?

Cheers Bastian
frijitz
wackelpeter wrote:
glennfin wrote:
I'm not sure but..... The dark arrows (top of the pots) connect to +V?
.....also, U4, U5, U6 the dark arrow pointing to these op-amps, what pin? +v rail?..... and the "X Y Z" are the outputs? Are these quad opamps? singles? what type did you use? TL074"s?
I'm thinking about breadboarding this but want to make sure I understand the all the connections.


Yes the dark arrows at the pots are connected to Ub+ (V+).

U1-U6 are OTA (LM13700,13600 or CA3080) these are the bias Inputs (1 and 16 on 13600+13700 or pin 5 on LM or CA3080. Means you will Need either 6 CA3080 or 3 of the LM13x00 dual OTA.

The TL07x means you can take whatever TL07xx OpAmp you have at hand there... You can use a single, dual or quad opAmp, depends on your taste and those available.

Actually there are 8 Outputs U,X,Y,Z and their inverted function -U,-X and so on.

A quick question to Ian, the rate control of this circuit should be useful for the Jerkster too, correct? I'm asking because i'm having sometimes hard times to find a sweet spot at the rate Settings and it goes easily with just a slight turn very fast. Already have increased the resistors for the Bias Input but not a multi-turn pot until now. Would this improve things a bit or should i go for an multiturn pot instead? Or perhaps change both?

Cheers Bastian

Glennfin -- Bastian answered your questions perfectly. Please let me know if you have any others.

Bastian -- Yes, you can use the CV circuits for the Jerkster. You might have to adjust the input offset resistors (summing node to PS) to get the range you like. If you need finer control you can add another pot (Fine) with a larger input resistor or use a 10-turn. I like separate Coarse and Fine controls, because a 10-turn you have to crank, and crank, and...

Ian
glennfin
I'm going to start breadboarding this but I have a few more questions.

I see a total of 6 pots which I assume are front panel controls;

R23 = gain
R25 = gain mod
R34 = damping
R36 = damping mod
R43 = rate
R45 = rate mod

And.... all the small circles marked with a small "a, b, c" are all external CV inputs? (a total of 7 cv inputs?)

Interconnect between sections marked with an apostrophe ' ?

Thanks and sorry for the dumb questions.. hmmm.....
wackelpeter
there are actually 7 pots without the one of the 2nd shaping Option. Ian describes the trim pot a few Posts above.

The a Output of Q4 a (first schematic bottom right Corner) goes to the four Bias Inputs of the OTA's via the 10k resistors.

The sections with the apostrophe are connected together, correct.
See one of my questions above and Ian's reply.

Also looking at the block Diagramm makes it a bit more clearer.
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